A Focus on Fractions
This book for K-8 mathematics educators explains cognitive research on how students develop their understanding of fraction concepts. It uses student work samples and classroom vignettes to show teachers how to reveal students' thinking in order to guide their development of fractional reasoning.
Uncomplicating Fractions to Meet Common Core Standards in Math, K-7
This book is organized by grade level. In each section, the relevant standard is presented, followed by a discussion of important underlying ideas associated with that standard. Also included are thoughtful, concept-based questions that can be used for classroom instruction, practice, or assessment.
Putting Essential Understanding of Fractions into Practice Grades 3-5
This book focuses on the pedagogical content knowledge needed to teach fractions effectively. It is written primarily for teachers in grades 3-5, but middle school teachers will find much in here to help their students who are struggling with fractions.
Developing Effective Fractions Instruction for Kindergarten Through 8th Grade
This practice guide presents five recommendations intended to help educators improve students’ understanding of fractions. Recommendations include strategies to develop young children’s understanding of early fraction concepts and ideas for helping older children understand the meaning of fractions and the computations involved. The guide also highlights ways to build on students’ existing strategies to solve problems involving ratios, rates, and proportions.
Minilessons for Operations with Fractions, Decimals, and Percents
This book provides number strings to exploring the four operations with fractions, decimals and percents. It draws upon several models including the double open number line, ratio table, and clock. An overview of the book is available for download. This contains some wonderful information!
Common Core Math in a PLC at Work, Grades 6-8
This teacher guide illustrates how to sustain successful implementation of the Common Core State Standards for mathematics, grades 6–8. Discover what students should learn and how they should learn it at each grade level. Comprehensive research-affirmed analysis tools and strategies will help you and your collaborative team develop and assess student demonstrations of deep conceptual understanding and procedural fluency.
Teaching Channel Fractions with Borrowing
Teaching Channel video featuring 4th graders using decomposition to subtract fractions with mixed numbers (borrowing).
Table of Contents
Books
A Focus on Fractions
This book for K-8 mathematics educators explains cognitive research on how students develop their understanding of fraction concepts. It uses student work samples and classroom vignettes to show teachers how to reveal students' thinking in order to guide their development of fractional reasoning.
Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 6-8
The latest edition of this excellent series is aligned to the Common Core.
Uncomplicating Fractions to Meet Common Core Standards in Math, K-7
This book is organized by grade level. In each section, the relevant standard is presented, followed by a discussion of important underlying ideas associated with that standard. Also included are thoughtful, concept-based questions that can be used for classroom instruction, practice, or assessment.
Putting Essential Understanding of Fractions into Practice Grades 3-5
This book focuses on the pedagogical content knowledge needed to teach fractions effectively. It is written primarily for teachers in grades 3-5, but middle school teachers will find much in here to help their students who are struggling with fractions.
Developing Effective Fractions Instruction for Kindergarten Through 8th Grade
This practice guide presents five recommendations intended to help educators improve students’ understanding of fractions. Recommendations include strategies to develop young children’s understanding of early fraction concepts and ideas for helping older children understand the meaning of fractions and the computations involved. The guide also highlights ways to build on students’ existing strategies to solve problems involving ratios, rates, and proportions.
Minilessons for Operations with Fractions, Decimals, and Percents
This book provides number strings to exploring the four operations with fractions, decimals and percents. It draws upon several models including the double open number line, ratio table, and clock. An overview of the book is available for download. This contains some wonderful information!
Using Formative Assessment to Differentiate Mathematics Instruction: Seven Practices to Maximize Learning
The author presents a very clear and easy to follow strategy for using formative assessment to differentiate math instruction. Included are sample preassessments, classroom management strategies, and a variety of forms to make differentiated instruction an integral part of your instruction.
Common Core Math in a PLC at Work, Grades 6-8
This teacher guide illustrates how to sustain successful implementation of the Common Core State Standards for mathematics, grades 6–8. Discover what students should learn and how they should learn it at each grade level. Comprehensive research-affirmed analysis tools and strategies will help you and your collaborative team develop and assess student demonstrations of deep conceptual understanding and procedural fluency.
Math Tools: 64 Ways to Differentiate Instruction and Increase Student Engagement
Organized around four distinct learning styles, this resource provides 64 instructional tools linked to NCTM process standards and offers guidelines for designing powerful, differentiated lessons. (There is a newer version of this book that is correlated to CCSSM.)
Videos
Teaching ChannelFractions with Borrowing
Teaching Channel video featuring 4th graders using decomposition to subtract fractions with mixed numbers (borrowing).
Multiplying Whole Numbers and Fractions
Teaching Channel video - extend understanding of multiplication as repeated addition
A Passion for Fractions
Teaching Channel video showcasing a fifth grade math class learning to multiply a fraction by a fraction.
Illustrative Mathematics
Fractions Progression Module
Initiatives
AMSTI - Alabama, Math, Science, and Technology Initiative
OGAP - Ongoing Assessment Project
Bibliography
Common Core Standards Writing Team. (2013, March 1). //Progressions for the Common Core State Standards in Mathematics// (draft). Tucson, AZ: Institute for Mathematics and Education, University of Arizona.
Common Core State Standards Initiative (CCSSI). 2010. Common core state standards for mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf
Daro, P., McCallum, W., and Zimba, J. (2012, February 16). The structure is the standards. Retrieved from http://commoncoretools.me/2012/02/16/the-structure-is-the-standards/
Chval, K., Lannin, J., Jones, D., & Dougherty, B. (2013). Putting essential understandings of fractions into practice. Reston, VA: National Council of Teachers of Mathematics.
Fennell, F. //Fractions - Let's get this started!//
http://www.serve.org/fractions.aspx
Imm, Fosnot, & Uittenbogaard (2007). Minilessons for Operations with Fractions, Decimals and Percents. Heinemann Press.
Laud, L. (2011). Using formative assessment to differentiate mathematics instruction grades 4-10: seven practices to maximize learning. Thousand Oaks, CA: Corwin.
National Mathematics Advisory Panel (2008). Foundations for Success: The Final Report of the National Mathematics Advisory Panel.
Washington, DC: U.S. Department of Education.
Parrish, S. (2010). Number talks: helping children build mental math and computation strategies. Sausalito, CA: Math Solutions.
Petit, M., Laird, R., & Marsden, E. (2010). A focus on fractions: bringing research into the classroom. New York: Routledge.
Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., & Wray., J. (2010). Developing effective fractions instruction for kindergarten through 8th grade: a practice guide. (NCEE#2010-4039). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.
Small, M. (2014). Uncomplicating fractions to meet common core standards in math, K-7. New York: Teachers College Press.
Van de Walle, J., Bay-Williams, J., Lovin, L, and Karp, K. (2014). Teaching student centered mathematics: developmentally appropriate instruction for grades 6-8. Boston: Pearson.
Van de Walle, J., Karp, K., and Bay-Williams, J. (2013). Elementary and middle school mathematics: teaching developmentally. Boston: Pearson.
Van de Walle, J. Lovin, L. (2006). Teaching student-centered mathematics: grades 5-8. Boston: Pearson.
Other Resources
F.U.N. Number Line
Visual Fractions website
California Mathematics Project Fractions Task Force
Rational Number Reasoning Database
Collection of articles and books - 190 items for fractions.
https://grade3commoncoremath.wikispaces.hcpss.org/
https://grade4commoncoremath.wikispaces.hcpss.org/
https://grade5commoncoremath.wikispaces.hcpss.org/
https://grade6commoncoremath.wikispaces.hcpss.org/Unit+2+The+Number+System
https://grade7commoncoremath.wikispaces.hcpss.org/
http://www.commoncoreworks.org/domain/121
Bits and Pieces I, II, and III - from Connected Mathematics
Name That Portion/ What's My Portion - from Investigations